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Asked by g_archanasharma | 19 Mar, 2019, 10:01: PM
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G i v e n colon space f left parenthesis x right parenthesis equals 1 minus 2 sin squared x space a n d space g left parenthesis x right parenthesis equals cos space 2 x space for all space f colon R rightwards arrow left square bracket negative 1 comma 1 right square bracket space a n d space g colon R rightwards arrow left square bracket negative 1 comma 1 right square bracket N o w comma space H left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals fraction numerator 1 minus 2 sin squared x over denominator cos space 2 x end fraction equals fraction numerator cos space 2 x over denominator cos space 2 x end fraction space..... space S i n c e space 1 minus 2 sin squared x equals cos space 2 x space equals 1 rightwards double arrow R a n g e space o f space H left parenthesis x right parenthesis space i s space left curly bracket 1 right curly bracket A l s o comma space x space c a n space t a k e space a n y space r e a l space v a l u e space i n space f space a n d space g space a n d space n o t space a f f e c t i n g space H left parenthesis x right parenthesis H e n c e comma space d o m a i n space o f space H left parenthesis x right parenthesis space i s space s e t space o f space a l l space r e a l space n u m b e r s space i. e. space R.
Answered by Renu Varma | 20 Mar, 2019, 04:20: PM

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